My take on it :
Curly was brought there with Jenka's knowledge. Curly was probably in better shape than Quote, and awoke in that house and secretly given the Colons to look after. My theory is that perhaps Jenka had believed that someday she might be the one who could break her brother's tortured cursed immortality, something that she hadn't been willing or perhaps able to do.
I'd like to believe Curly (and Quote) played an roles in ending the War. That whatever happened after wounding Miakid brought Curly under Jenka's watch. After all, when Curly woke up in Sand Zone, with possibly very young Mimiga children (just babies (or were they old enough to survive on their own?)), it's possible that the only other living person in Sand Zone was Jenka. And at least we know that the Colons used to visit Jenka.
I believe it's far too much of a coincidence to wake up in an empty zone with someone like Jenka nearby.
As for the house; I believe the Sand Zone wasn't always such a desolate dead place. That partially covered bar, or house that Curly and the Colons have taken residence in; was probably just the tip of a much larger town, now lost and buried; reclaimed by the sand or cave. I also have a theory that Sand Zone was once more of an oasis, rather than some kind of necromancer's desert full of walking bones. Maybe after the water stopped flowing from construction by scientists and robots with the waterway, or maybe after Jenka grew old and weak... the Paradise (Oasis) Zone, turned to dust with time.
Why was that one building still there? Perhaps someone had a hand in unburying it...? Jenka or a team of digging puppies... It would be the perfect place to keep Curly close.
Quote's fate on the other hand... I'm undecided. It does seem FAR too much a coincidence that some kind of incredible gunsmith, capable of making the Spur; just happens to be a stones throw away from where Quote wakes up. (Curly wakes up near an incredible witch, pivotal to the events occuring on the island; and Quote apparently was resting about the same distance away from the Spur making Gunsmith? ...)
Whether or not the Gunsmith had a role in Quote's awakening (did he repair him?), or if there's something else at play, I'm not sure... It seems suspicious that the only evil red Eye door on the island we see, happens to be at the entrance of the Cave that Quote and the Gunsmith. I must at least wonder of a different possibility... That if someone sealed Quote and the Gunsmith in that cave. That what if the Gunsmith had been asleep for as long as Quote has?
But, who would have sealed them in that place... and why; and how was Quote able to awaken? Such a strange watching Eye door...
Anyway, ignoring the strange door, I *used* to believe Quote was buried in that cave. And that his awakening was like Quote breaking out of his tomb. It's possible that a Mimiga could have buried him there, thinking he was permantantly dead. Mimiga Village is just around the corner...
I might imagine that although most Mimigas hated robots, there were a few that knew what Quote did for them, and maybe brought him there to rest.
Alternatively, Quote could have been in cave-in... The waterway is probably not too far away after all, since the reservoir connects to it. Something could have happened that lead him there. And perhaps a simple bump on the head ....
....................................... The story is yours to choose.